Symmetry and order in systems chemistry

Bistable Functions and Signaling Motifs in Systems Chemistry: Taking the Next Step Toward Synthetic Cells

A key challenge in modern chemistry research is to mimic life-like functions using simple molecular networks and the integration of such networks into the first functional artificial cell. Central to this endeavor is the development of signaling elements that can regulate the cell function in time and space by producing entities of code with specific information to induce downstream activity. Such artificial signaling motifs can emerge in nonequilibrium systems, exhibiting complex dynamic behavior like bistability, multistability, oscillations, and chaos. However, the de novo, bottom-up design of such systems remains challenging, primarily because the kinetic characteristics and energy aspects yielding bifurcation have not yet been globally defined. We herein review our recent work that focuses on the design and functional analysis of peptide-based networks, propelled by replication reactions and exhibiting bistable behavior. Furthermore, we rationalize and discuss their exploitation and implementation as variable signaling motifs in homogeneous and heterogeneous environments.The bistable reactions constitute reversible second-order autocatalysis as positive feedback to generate two distinct product distributions at steady state (SS), the low-SS and high-SS. Quantitative analyses reveal that a phase transition from simple reversible equilibration dynamics into bistability takes place when the system is continuously fueled, using a reducing agent, to keep it far from equilibrium. In addition, an extensive set of experimental, theoretical, and simulation studies highlight a defined parameter space where bistability operates.Analogous to the arrangement of protein-based bistable motifs in intracellular signaling pathways, sequential concatenation of the synthetic bistable networks is used for signal processing in homogeneous media. The cascaded network output signals are switched and erased or transduced by manipulating the order of addition of the components, allowing it to reach "on demand" either the low-SS or high-SS. The pre-encoded bistable networks are also useful as a programming tool for the downstream regulation of nanoscale materials properties, bridging together the Systems Chemistry and Nanotechnology fields. In such heterogeneous cascade pathways, the outputs of the bistable network serve as input signals for consecutive nanoparticle formation reaction and growth processes, which-depending on the applied conditions-regulate various features of (Au) nanoparticle shape and assembly.Our work enables the design and production of various signaling apparatus that feature higher complexity than previously observed in chemical networks. Future studies, briefly discussed at the end of the Account, will be directed at the design and analysis of more elaborate functionality, such as bistability under flow conditions, multistability, and oscillations. We propose that a profound understanding of the design principles facilitating the replication-based bistability and related functions bear implications for exploring the origin of protein functionality prior to the highly evolved replication-translation-transcription machinery. The integration of our peptide-based signaling motifs within future synthetic cells seems to be a straightforward development of the two alternating states as memory and switch elements for controlling cell growth and division and even communication among different cells. We furthermore suggest that such systems can be introduced into living cells for various biotechnology applications, such as switches for cell temporal and spatial manipulations.

Open Prebiotic Environments Drive Emergent Phenomena and Complex Behavior

We have been studying simple prebiotic catalytic replicating networks as prototypes for modeling replication, complexification and Systems Chemistry. While living systems are always open and function far from equilibrium, these prebiotic networks may be open or closed, dynamic or static, divergent or convergent to a steady state. In this paper we review the properties of these simple replicating networks, and show, via four working models, how even though closed systems exhibit a wide range of emergent phenomena, many of the more interesting phenomena leading to complexification and emergence indeed require open systems.

The Influence of Modularity, Seeding, and Product Inhibition on Peptide Autocatalytic Network Dynamics

Chemical networks often exhibit emergent, systems-level properties that cannot be simply derived from the linear sum of the individual components. The design and analysis of increasingly complex chemical networks thus constitute a major area of research in Systems Chemistry. In particular, much research is focused on the emergence of functional properties in prebiotic chemical networks relevant to the origin and early evolution of life. Here, we apply a formal framework known as RAF theory to study the dynamics of a complex network of mutually catalytic peptides. We investigate in detail the influence of network modularity, initial template seeding, and product inhibition on the network dynamics. We show that these results can be useful for designing new experiments, and further argue how they are relevant to origin of life studies.

Bistability and Bifurcation in Minimal Self-Replication and Nonenzymatic Catalytic Networks

Bistability and bifurcation, found in a wide range of biochemical networks, are central to the proper function of living systems. We investigate herein recent model systems that show bistable behavior based on nonenzymatic self-replication reactions. Such models were used before to investigate catalytic growth, chemical logic operations, and additional processes of self-organization leading to complexification. By solving for their steady-state solutions by using various analytical and numerical methods, we analyze how and when these systems yield bistability and bifurcation and discover specific cases and conditions producing bistability. We demonstrate that the onset of bistability requires at least second-order catalysis and results from a mismatch between the various forward and reverse processes. Our findings may have far-reaching implications in understanding early evolutionary processes of complexification, emergence, and potentially the origin of life.

Theoretical Models of Generalized Quasispecies

Theoretical modeling of quasispecies has progressed in several directions. In this chapter, we review the works of Emmanuel Tannenbaum, who, together with Eugene Shakhnovich at Harvard University and later with colleagues and students at Ben-Gurion University in Beersheva, implemented one of the more useful approaches, by progressively setting up various formulations for the quasispecies model and solving them analytically. Our review will focus on these papers that have explored new models, assumed the relevant mathematical approximations, and proceeded to analytically solve for the steady-state solutions and run stochastic simulations . When applicable, these models were related to real-life problems and situations, including changing environments, presence of chemical mutagens, evolution of cancer and tumor cells , mutations in Escherichia coli, stem cells , chromosomal instability (CIN), propagation of antibiotic drug resistance , dynamics of bacteria with plasmids , DNA proofreading mechanisms, and more.

Robustness of synthetic circadian clocks to multiple environmental changes

A molecular network that mimics circadian clocks from cyanobacteria is constructed in silico. Simulating its oscillatory behaviour under variable conditions reveals its robustness relative to networks of alternative topologies. The principles for synthetic chemical circadian networks to work properly are consequently highlighted.

Coupled Oscillations and Circadian Rhythms in Molecular Replication Networks

Living organisms often display rhythmic and oscillatory behavior. We investigate here a challenge in contemporary Systems Chemistry, that is, to construct "bottom-up" molecular networks that display such complex behavior. We first describe oscillations during self-replication by applying kinetic parameters relevant to peptide replication in an open environment. Small networks of coupled oscillators are then constructed in silico, producing various functions such as logic gates, integrators, counters, triggers, and detectors. These networks are finally utilized to simulate the connectivity and network topology of the Kai proteins circadian clocks from the S. elongatus cyanobacteria, thus producing rhythms whose constant frequency is independent of the input intake rate and robust toward concentration fluctuations. We suggest that this study helps further reveal the underlying principles of biological clocks and may provide clues into their emergence in early molecular evolution.

Growth and division in a dynamic protocell model

In this paper a new model of growing and dividing protocells is described, whose main features are (i) a lipid container that grows according to the composition of the molecular milieu (ii) a set of “genetic memory molecules” (GMMs) that undergo catalytic reactions in the internal aqueous phase and (iii) a set of stochastic kinetic equations for the GMMs. The mass exchange between the external environment and the internal phase is described by simulating a semipermeable membrane and a flow driven by the differences in chemical potentials, thereby avoiding to resort to sometimes misleading simplifications, e.g., that of a flow reactor. Under simple assumptions, it is shown that synchronization takes place between the rate of replication of the GMMs and that of the container, provided that the set of reactions hosts a so-called RAF (Reflexive Autocatalytic, Food-generated) set whose influence on synchronization is hereafter discussed. It is also shown that a slight modification of the basic model that takes into account a rate-limiting term, makes possible the growth of novelties, allowing in such a way suitable evolution: so the model represents an effective basis for understanding the main abstract properties of populations of protocells.

Model identification of a template-directed peptide network for optimization in a continuous reactor

With an open driven system, the chemical network can be controlled to new nonequilibrium steady states.

Autocatalyses

Autocatalysis is a fundamental concept, used in a wide range of domains. From the most general definition of autocatalysis, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. With the notion of autocatalysis covering a large variety of mechanistic realizations with very similar behaviors, it is proposed that the key signature of autocatalysis is its kinetic pattern expressed in a mathematical form.

Autocatalysis: at the root of self-replication

Autocatalysis is a fundamental concept, used in a wide range of domains. From its most general definition, that is, a process in which a chemical compound is able to catalyze its own formation, several different systems can be described. We detail the different categories of autocatalyses, and compare them on the basis of their mechanistic, kinetic, and dynamic properties. It is shown how autocatalytic patterns can be generated by different systems of chemical reactions. The notion of autocatalysis covers a large variety of mechanistic realizations with very similar behaviors; it is proposed that its key signature is its kinetic pattern expressed in a mathematical form. This notion, while describing dynamic behaviors at the most fundamental level, is at the basis for developing higher-level concepts towards life: autocatalytic sets, and autopoietic systems.

Elucidating the origin of diastereoselectivity in a self-replicating system: selfishness versus altruism

We have investigated a diastereoselective self-replicating system based on a cycloaddition of a fulvene derivative and a maleimide using a two-pronged approach of combining NMR spectroscopy with computational modelling. Two diastereomers are formed with identical rates in the absence of replication. When replication is enabled, one diastereomer takes over the resources as a "selfish" autocatalyst, while exploiting the competitor as a weak "altruist", resulting in a diastereoselectivity of 16:1. We applied 1D and 2D NMR spectroscopic techniques supported by ab initio chemical shifts as well as ab initio molecular dynamics simulations to study the structure and dynamics of the underlying network. This powerful combination allowed us to decipher the energetic and structural rationale behind the observed behaviour, while static computational methods currently used in the field did not.

Energy sources, self-organization, and the origin of life

The emergence and early developments of life are considered from the point of view that contingent events that inevitably marked evolution were accompanied by deterministic driving forces governing the selection between different alternatives. Accordingly, potential energy sources are considered for their propensity to induce self-organization within the scope of the chemical approach to the origin of life. Requirements in terms of quality of energy locate thermal or photochemical activation in the atmosphere as highly likely processes for the formation of activated low-molecular weight organic compounds prone to induce biomolecular self-organization through their ability to deliver quanta of energy matching the needs of early biochemical pathways or the reproduction of self-replicating entities. These lines of reasoning suggest the existence of a direct connection between the free energy content of intermediates of early pathways and the quanta of energy delivered by available sources of energy.

A simple network of synthetic replicators can perform the logical OR operation

A small network of synthetic replicators is capable of responding to instructional inputs such that the output of the network is an excess of one of the replicators whenever the input contains either or both of the replicators, mirroring the OR boolean logic operation.

Second order catalytic quasispecies yields discontinuous mean fitness at error threshold

The quasispecies model describes processes related to the origin of life and viral evolutionary dynamics. We discuss how the error catastrophe that reflects the transition from localized to delocalized quasispecies population is affected by catalytic replication of different reaction orders. Specifically, we find that second order mechanisms lead to a discontinuity in the mean fitness of the population at the error threshold. This is in contrast to the behavior of the first order, autocatalytic replication mechanism considered in the standard quasispecies model. This suggests that quasispecies models with higher order replication mechanisms produce discontinuities in the mean fitness, and hence the viable population fraction as well, at the error threshold, while lower order replication mechanisms yield a continuous mean fitness function. We discuss potential implications for understanding replication in the RNA world and in virology.

Homochirality and the need for energy

The mechanisms for explaining how a stable asymmetric chemical system can be formed from a symmetric chemical system, in the absence of any asymmetric influence other than statistical fluctuations, have been developed during the last decades, focusing on the non-linear kinetic aspects. Besides the absolute necessity of self-amplification processes, the importance of energetic aspects is often underestimated. Going down to the most fundamental aspects, the distinction between a single object-that can be intrinsically asymmetric-and a collection of objects-whose racemic state is the more stable one-must be emphasized. A system of strongly interacting objects can be described as one single object retaining its individuality and a single asymmetry; weakly or non-interacting objects keep their own individuality, and are prone to racemize towards the equilibrium state. In the presence of energy fluxes, systems can be maintained in an asymmetric non-equilibrium steady-state. Such dynamical systems can retain their asymmetry for times longer than their racemization time.